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statistics principles and methods

Questions and Answers of Statistics Principles And Methods

=+Responses consistent with percentages given in the article for the samples from Italy, Spain, France, the United States, and South Korea are summarized in the accompanying table. Based on these
=+12.18 ● In November 2005, an international study to assess public opinion on the treatment of suspected terrorists was conducted (“Most in U.S., Britain, S. Korea and France Say Torture Is OK
=+Insight, March 24, 2006). Is there evidence that the proportion falling in the three credit card response categories is not the same for all three years? Test the relevant hypotheses using a .05
=+12.17 ● ▼ The polling organization Ipsos conducted telephone surveys in March of 2004, 2005, and 2006. In each year, 1001 people age 18 or older were asked about whether they planned to use a
=+what would you conclude if X 2 5 14.5 and a 5 .05?
=+b. If there were only four candidates vying for election,
=+2 5 7.2, what would you conclude at significance level .10?
=+12.16 A random sample of 1000 registered voters in a certain county is selected, and each voter is categorized with respect to both educational level (four categories) and preferred candidate in an
=+c. How does your answer in Part (a) change if there are four rather than three categories for political philosophy?
=+b. How does your answer in Part (a) change if there are seven campuses rather than six?
=+a. On how many degrees of freedom will the resulting X 2test be based?
=+12.15 A particular state university system has six campuses. On each campus, a random sample of students will be selected, and each student will be categorized with respect to political philosophy
=+Use the goodness-of-fit test with significance level .10 to determine whether the data are consistent with this hypothesis.
=+12.14 ● It is hypothesized that when homing pigeons are disoriented in a certain manner, they will exhibit no preference for any direction of flight after takeoff. To test this, 120 pigeons are
=+Frequency 926 288 293 104 Mendel’s laws of inheritance imply that p1 5 9/16, p2 5 3/16, p3 5 3/16, and p4 5 1/16. Are the data from this experiment consistent with Mendel’s laws? Use a .01
=+12.13 ▼ The article “Linkage Studies of the Tomato”(Transactions of the Royal Canadian Institute [1931]:1–19) reported the accompanying data on phenotypes resulting from crossing tall
=+. How would your analysis and conclusion differ from those in Part (a)?
=+b. Suppose that a random sample of 300 plants had resulted in the same value of X 2
=+a. Carry out a test of the null hypothesis that the theory is correct, using level of significance a 5 .05.
=+12.12 A certain genetic characteristic of a particular plant can appear in one of three forms (phenotypes). A researcher has developed a theory, according to which the hypothesized proportions
=+, and p3 are the true proportions of all returned questionnaires accompanied by cover letters I, II, and III, respectively. Use a .05 significance level.Cover-letter Type I II III Frequency 48 44
=+Suppose that each of the three cover letters accompanied questionnaires sent to an equal number of randomly selected students. Returned questionnaires were then classified according to the type
=+cover letters were used in a survey of students at a Midwestern university (“The Effectiveness of Cover-Letter Appeals,” Journal of Social Psychology [1984]: 85–91).
=+12.11 When public opinion surveys are conducted by mail, a cover letter explaining the purpose of the survey is usually included. To determine whether the wording of the cover letter influences the
=+Suppose that the data resulted from a random sample of 200 lottery ticket purchasers. Based on these sample data, is it reasonable to conclude that one or more of these three age groups buys a
=+between 35 and 64 years old, and 14% are 65 years old or older. The article also gave information on the age distribution of those who purchase lottery tickets. The following table is consistent
=+12.10 An article about the California lottery that appeared in the San Luis Obispo Tribune (Dec. 15, 1999) gave the following information on the age distribution of adults in California: 35% are
=+Do the data provide evidence of a color preference? Test using a 5 .01.
=+519–526) studied the pecking behavior of 1-day-old bobwhites. In an area painted white, they inserted four pins with different colored heads. The color of the pin chosen on the bird’s first
=+12.9 ● ▼ The color vision of birds plays a role in their foraging behavior: Birds use color to select and avoid certain types of food. The authors of the article “Colour Avoidance in Northern
=+Day of Week Frequency Sunday 14 Monday 13 Tuesday 12 Wednesday 15 Thursday 14 Friday 17 Saturday 15 Based on these data, is it reasonable to conclude that the proportion of accidents is not the
=+12.8 ● Each observation in a random sample of 100 bicycle accidents resulting in death was classified according to the day of the week on which the accident occurred.Data consistent with
=+c. Test the hypotheses proposed in Part (b) using a .05 significance level.
=+b. The null hypothesis in Part (a) specifies that fatal accidents were equally likely to occur in any of the 12 months.But not all months have the same number of days. What null and alternative
=+is the proportion of fatal bicycle accidents that occur in January, p2 is the proportion for February, and so on. Use a significance level of .01.
=+a. Use the given data to test the null hypothesis H0: p1 5 1/12, p2 5 1/12, . . . , p12 5 1/12, where p1
=+12.7 ● The report referenced in the previous exercise(“Fatality Facts 2004: Bicycles”) also classified 719 fatal bicycle accidents according to the month in which the accident occurred,
=+is the proportion occurring between noon and midnight. Do the given data provide evidence against this hypothesis, or are the data consistent with it? Justify your answer with an appropriate test.
=+hypothesis: H0: p1 5 1/3, p2 5 2/3, where p1 is the proportion of accidents occurring between midnight and noon and p2
=+b. Suppose a safety office proposes that bicycle fatalities are twice as likely to occur between noon and midnight as during midnight to noon and suggests the following
=+a. Assume it is reasonable to regard the 715 bicycle accidents summarized in the table as a random sample of fatal bicycle accidents in 2004. Do these data support the hypothesis that fatal
=+12.6 ● The report “Fatality Facts 2004: Bicycles” (Insurance Institute, 2004) included the following table classifying 715 fatal bicycle accidents according to time of day the accident
=+b. The null hypothesis from Part (a) specifies that half of male smokers of low-tar cigarettes began smoking between the ages of 16 and 20. Explain why p2 5 .2 and p3 5 .3 is consistent with the
=+are defined in a similar way for the other three age groups.
=+where p1 5 proportion of male low-tar cigarette smokers who started smoking before age 16, and p2, p3, and p4
=+a. Use a chi-square goodness-of-fit test to test the null hypothesis H0: p1 5 .25, p2 5 .2, p3 5 .3, p4 5 .25,
=+12.5 ● The paper referenced in the previous exercise also gave the accompanying data on the age at which smoking started for a sample of 1031 men who smoked low-tar cigarettes.
=+Assume it is reasonable to regard the sample as representative of male smokers who die of lung cancer. Is there convincing evidence that the proportion of male smoker lung cancer deaths is not the
=+who Tar Level Frequency 0–7 mg 103 8–14 mg 378 15–21 mg 563$22 mg 150
=+12.4 ● The paper “Cigarette Tar Yields in Relation to Mortality from Lung Cancer in the Cancer Prevention Study II Prospective Cohort” (British Medical Journal[2004]: 72–79) included the
=+b. If the random sample had consisted of only 40 nuts, would you use the chi-square test here? Explain your reasoning.
=+2 5 19.0, what conclusion would be appropriate for a significance level of .001?
=+a. If the sample size is 200 and the resulting test statistic value is X
=+12.3 Packages of mixed nuts made by a certain company contain four types of nuts. The percentages of nuts of Types 1, 2, 3, and 4 are supposed to be 40%, 30%, 20%, and 10%, respectively. A random
=+what would you conclude if X 2 5 13.7 and a test with a 5 .05 was used?
=+c. If there were six different covers rather than just four,
=+b. What conclusion would be appropriate at significance level .01 if X 2 5 15.3?
=+a. If the resulting X 2value were 6.4, what conclusion would you reach when using a test with significance level .05?
=+12.2 A particular paperback book is published in a choice of four different covers. A certain bookstore keeps copies of each cover on its racks. To test the hypothesis that sales are equally
=+12.1 From the given information in each case below, state what you know about the P-value for a chi-square test and give the conclusion for a significance level of a 5 .01.a. X 2 5 7.5, df 5 2d. X
=+11.18 ● The article “Movement and Habitat Use by Lake Whitefish During Spawning in a Boreal Lake: Integrating Acoustic Telemetry and Geographic Information Systems”(Transactions of the
=+11.28 Do certain behaviors result in a severe drain on energy resources because a great deal of energy is expended in comparison to energy intake? The article “The Energetic Cost of Courtship
=+necessary for your test to be valid.
=+two groups. The first group was the short-duration loneliness group, and the second was the long-duration loneliness group. A self-esteem inventory was administered to students in both groups.
=+11.27 The effect of loneliness among college students was examined in the article “The Importance of Perceived Duration: Loneliness and Its Relationship to Self-Esteem and Academic Performance”
=+Do these data support the researcher’s conclusion? Test the relevant hypotheses using a 5 .05. Can you conclude that heading the ball causes lower IQ?
=+whether they averaged 10 or more headers per game. Mean IQs were reported in the article, but the sample sizes and standard deviations were not given. Suppose that these values were as given in
=+11.26 A researcher at the Medical College of Virginia conducted a study of 60 randomly selected male soccer players and concluded that frequently “heading” the ball in soccer lowers players’
=+Use the following MINITAB output to determine whether the data indicate that the mean half-life is higher for those on a normal diet than those on a high-fiber diet. Assume that treatments were
=+this type have been carried out.)Sample Sample Sample Behavior Size Mean sd Noncourting 11 .072 .0066 Courting 15 .099 .0071
=+a. The pooled t test is a test procedure for testing H0: m1 2 m2 5 hypothesized value when it is reasonable to assume that the two population distributions are normal with equal standard deviations
=+c. Can you think of a reasonable method of collecting data that would result in independent samples? Would such an experiment be as informative as a paired experiment?Comment.
=+b. Does your method result in paired data?
=+a. Describe how you would go about collecting data for your investigation.
=+11.29 Suppose that you were interested in investigating the effect of a drug that is to be used in the treatment of patients who have glaucoma in both eyes. A comparison between the mean reduction
=+b. Would the conclusion in Part (a) have been different if the two-sample t test had been used rather than the pooled t test?
=+is true, the resulting pooled t statistic has a t distribution with df 5 n1 1 n2 2 2. For the reported data, the two sample standard deviations are similar. Use the pooled t test with a 5 .05 to
=+). The test statistic for the pooled t test is obtained by replacing both s1 and s2 in the two-sample t test statistic with sp where When the population distributions are normal with equal standard
=+25(OH)D3 in Subjects Receiving a High-Fibre Diet,”British Journal of Nutrition [1993]: 213–216).Normal diet 19.1 24.0 28.6 29.7 30.0 34.8 High-fiber diet 12.0 13.0 13.6 20.5 22.7 23.7 24.8
=+healthy individuals. One group was placed on a normal diet, whereas the second group was placed on a high-fiber diet. The accompanying table gives the resulting data(from “Reduced Plasma
=+of rape myths, so lower scores are considered desirable.The accompanying data appeared in the article “Rape Supportive Attitudes Among Greek Students Before and After a Date Rape Prevention
=+11.20 The Rape Myth Acceptance Scale (RMAS) was administered to 333 male students at a public university. Of these students, 155 were randomly selected from students who did not belong to a
=+c. Use a 90% confidence interval to estimate the difference in mean hardness for chicken chilled 2 hours before cooking and chicken chilled 8 hours before cooking.
=+b. Do the data suggest that there is a difference in mean hardness for chicken chilled 8 hours before cooking and chicken chilled 24 hours before cooking? Use a 5 .05.
=+a. Do the data suggest that there is a difference in mean hardness for chicken chilled 0 hours before cooking and chicken chilled 2 hours before cooking? Use a 5 .05.
=+the canned chicken, samples were evaluated by trained tasters. One characteristic of interest was hardness. The accompanying summary quantities were obtained. Each mean is based on 36
=+11.19 ▼ Techniques for processing poultry were examined in the article “Texture Profiles of Canned Boned Chicken as Affected by Chilling-Aging Times” (Poultry Science [1994]: 1475–1478).
=+939–952) included the accompanying data on weights of 10 fish caught in 1995 and 10 caught in 1996.1995 776 580 539 648 538 891 673 783 571 627 1996 571 627 727 727 867 1042 804 832 764 727 Is it
=+Mean RMAS Sample n Score sd Fraternity members 178 25.63 6.16 Not fraternity members 155 27.40 5.51
=+11.21 The discharge of industrial wastewater into rivers affects water quality. To assess the effect of a particular power plant on water quality, 24 water specimens were taken 16 km upstream and 4
=+11.25 ● British health officials have expressed concern about problems associated with vitamin D deficiency among certain immigrants. Doctors have conjectured that such a deficiency could be
=+with these summary quantities, appear in the table at the top of the page.The authors of the article assumed in their analysis of the data that both force distributions (advanced and intermediate)
=+11.24 ● Tennis elbow is thought to be aggravated by the impact experienced when hitting the ball. The article“Forces on the Hand in the Tennis One-Handed Backhand” (International Journal of
=+how often they drank alcoholic beverages. For the sorority rush group, the mean was 2.72 drinks per week and the standard deviation .86. For the group who did not rush, the mean was 2.11 and the
=+11.23 The article “The Sorority Rush Process: SelfSelection, Acceptance Criteria, and the Effect of Rejection” (Journal of College Student Development [1994]:346–353) reported on a study of
=+level is lower for those who have attempted suicide? Test the relevant hypotheses using a 5 .05.
=+attempted suicide, the mean cholesterol level was 198.The mean cholesterol level of 331 randomly selected patients admitted to the hospital for other reasons was 217.The sample standard deviations
=+11.22 According to the Associated Press (San Luis Obispo Telegram-Tribune, June 23, 1995), a study by Italian researchers indicated that low cholesterol and depression were linked. The
=+11.31 ● ▼ To determine if chocolate milk was as effective as oth b h d t l t d i k i l clist and clist exha clist
=+On one day the drink provided was chocolate milk and on the other day the drink provided was a carbohydrate replacement drink. Data consistent with summary quantities appearing in the paper “The

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